A public resource configuration and use collaborative optimization method based on hypergraph game

Abstract

The application discloses a public resource configuration and use collaborative optimization method based on a hypergraph game, relates to the field of public goods game, and comprises the following steps: a hypergraph public resource game model is constructed, the hypergraph node is a participant, the hyperedge is a public resource item, and the participation relationship is described by a hypergraph correlation matrix; the income of each subject under different cooperation states is calculated according to the hypergraph model; the income of the subject is calculated according to a linear public good income function, and the threshold of the subject is calculated by using the full cooperation maintenance condition under the Grim strategy; the resource allocation and contribution strategy are optimized, and the resource allocation scheme and individual contribution scheme beneficial to maintaining full cooperation are output. The application uses a hypergraph to represent multi-person high-order interaction, is more accurate than a common graph model in describing the real structure of multiple subjects participating in a public item, uses a full cooperation threshold and a feasible interval to judge stability, is more interpretable, and provides resource allocation optimization and contribution matrix optimization, serving managers and participant subjects.

Description

Technical Field

[0001] This invention relates to the field of public goods game theory, and more particularly to a collaborative optimization method for the allocation and use of public resources based on hypergraph game theory. Background Technology

[0002] In networked systems such as climate governance, cross-regional water resource sharing, public infrastructure construction, renewable resource management, public health collaboration, and online group cooperation, multiple stakeholders typically need to collaborate long-term around limited resources. Each stakeholder can either invest its own resources in joint projects to improve overall benefits or choose to retain resources for short-term individual gains. Therefore, without effective mechanism design or strategic guidance, the system is prone to problems such as free-riding, insufficient investment, shifting of responsibility, breakdown of cooperation, and inefficient use of public resources.

[0003] The aforementioned problems exhibit clear network characteristics. On the one hand, the actors are not isolated from each other; the resource input of one actor affects the returns of other actors, and the input behavior of other actors, in turn, influences the decision-making of the first actor. On the other hand, collaboration among actors is usually not a one-off event but occurs continuously through multiple rounds of interaction. Actors adjust their input strategies based on historical returns, the behavior of others, expectations of future cooperation, and institutional constraints. Therefore, determining whether a networked system can maintain long-term cooperation, identifying the actors most likely to deviate from cooperation, and promoting full cooperation through resource allocation and input ratio adjustments are important technical issues in the governance of complex systems.

[0004] Public goods game theory is a commonly used model for studying the aforementioned problems. In classic public goods game theory, multiple participants decide whether to contribute their resources to a common pool. The resources in the pool are then amplified through a certain level of productivity before being returned to the participants. This model reveals the contradiction between collective optimality and individual rationality: from a collective perspective, full contribution from all stakeholders increases the overall system benefit; however, from an individual perspective, reducing or not contributing may bring short-term private gains. This contradiction is one of the fundamental reasons why cooperation is difficult to maintain in public governance, resource sharing, and group collaboration.

[0005] Therefore, those skilled in the art are dedicated to developing a collaborative optimization method for the allocation and use of public resources based on hypergraph games. Summary of the Invention

[0006] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is that most existing public goods game and network game methods are based on ordinary graphs or homogeneous groups, which makes it difficult to express the high-order interaction structure of a public project in which multiple subjects participate and the same subject participates in multiple projects at the same time.

[0007] To achieve the above objectives, this invention provides a collaborative optimization method for the allocation and use of public resources in hypergraph games, the method comprising the following steps: S101: Construct a hypergraph public resource game model. In the hypergraph public resource game model, hypergraph nodes are participating entities, and hyperedges are public resource projects. The participation relationship between the participating entities and the public resource projects is described by the hypergraph association matrix. S103: Based on the hypergraph public resource game model, calculate the payoffs of each participating entity under different cooperative states; S105: Calculate the revenue of the participating entity based on the linear public goods revenue function, and calculate the threshold of the participating entity using the full cooperation maintenance condition under the Grim strategy; S107: Optimize resource allocation and contribution strategies, and output resource allocation and individual contribution schemes that are conducive to maintaining full cooperation.

[0008] Further, step S103 includes the following sub-steps: S1031: Calculate the revenue of the participating entity under a given contribution matrix based on the linear public goods revenue function; S1032: Construct three types of cooperative states, including the state in which all participating entities fully cooperate, the state in which some participating entities deviate from the cooperation while other participating entities maintain full cooperation, and the state in which none of the participating entities contribute. S1033: Calculate the revenue of the participating entities under the three types of cooperative states, and use the revenue as the threshold for calculating the full cooperation of the participating entities.

[0009] Furthermore, the linear public good revenue function is:

[0010] in, as the main body Given a contribution matrix The following profits, as the main body Resource endowment, as the main body Participating in the A game of public resources as the main body Productivity parameters, as the main body In the The proportion of contribution to public resources, For the contribution matrix, For public resource identification, For the number of public resource games, For the number of participating entities, For super-edge size.

[0011] Further, in step S105, under the Grim policy, full cooperation is maintained under the following condition:

[0012] in, remember To exclude the main body Maintain full cooperation with other entities, main body Deviating from the benefits of full cooperation The revenue when no entity contributes. The benefits when all parties cooperate fully. For the probability of continuation.

[0013] Furthermore, the threshold for the participating entity is:

[0014] The threshold for cooperation among all participating entities in the system is:

[0015] in, as the main body Full cooperation threshold The threshold for cooperation among all participating entities.

[0016] Furthermore, in step S107, when the continuation probability meets a preset condition, the resource endowment vector or contribution matrix is ​​adjusted to lower the overall cooperation threshold of all participating entities or expand the feasible range of full cooperation, thereby obtaining a resource allocation scheme and individual contribution scheme that are conducive to maintaining full cooperation. The preset condition is:

[0017] in, To maintain probability, The threshold for cooperation among all participating entities.

[0018] Further, step S107 includes the following sub-steps: S1071: Identify high-threshold nodes and determine optimization directions; S1072: Based on the extent, threshold size, and resource endowment of the participating entities, the resource endowment is redistributed; S1073: By adjusting the contribution matrix, the proportion of investment by the participating entities in different public goods projects is changed to promote full cooperation.

[0019] Furthermore, in step S1071, based on the threshold calculation results of the participating entities, all participating entities are sorted, key entities that cause the overall system threshold to rise are identified, the thresholds of high-threshold entities are lowered, and the resource or contribution configurations of low-threshold entities are appropriately adjusted without compromising overall feasibility, so that the thresholds of each entity are more balanced, thereby reducing the maximum threshold of the system.

[0020] Furthermore, in step S1072, when redistributing resource endowments, more resources are directed to the participating entities or key hyperedge associated entities that can effectively reduce the overall cooperation threshold of all participating entities, thereby reducing the overall cooperation threshold of the system.

[0021] Furthermore, in step S1073, when adjusting the contribution matrix, the participating entities with larger super-degree, more abundant resources, or higher cooperation stability are guided to allocate more contributions to the super-edges where entities with lower average super-degree, higher cooperation risk, or higher threshold reside.

[0022] In a preferred embodiment of the present invention, compared with the prior art, the present invention has the following beneficial technical effects: 1. This invention uses the subject as the node and public goods projects, governance alliances or collaborative groups as the hyperedges. It represents the participation relationship between the subject and the project through an association matrix and introduces resource endowment, contribution matrix, project productivity and continuation probability. It can completely preserve the interaction and overlapping participation information of multiple groups and avoid structural distortion caused by breaking high-order collaborative relationships into binary edges. 2. This invention proposes a method for calculating the feasible interval of full cooperation and the node-level continuation probability threshold, which transforms the cooperation stability problem into a threshold comparison problem, and can quickly identify whether full cooperation is feasible and the bottleneck subject most likely to deviate from cooperation.

[0023] The following will further explain the concept, specific structure, and technical effects of the present invention in conjunction with the accompanying drawings, so as to fully understand the purpose, features, and effects of the present invention. Attached Figure Description

[0024] Figure 1 This is a preferred embodiment of the collaborative optimization method implementation steps of the present invention; Figure 2 This is a schematic diagram of a collaborative optimization method according to a preferred embodiment of the present invention; Figure 3 This is a schematic diagram of a hypergraph public goods game structure according to a preferred embodiment of the present invention.

[0025] Explanation of the numbering in the diagram: 1-7 are the participating main nodes. Detailed Implementation

[0026] The following description, with reference to the accompanying drawings, illustrates several preferred embodiments of the present invention to make its technical content clearer and easier to understand. The present invention can be embodied in many different forms, and the scope of protection of the present invention is not limited to the embodiments mentioned herein.

[0027] In the accompanying drawings, components with the same structure are indicated by the same numerical designation, and components with similar structures or functions are indicated by similar numerical designations. The dimensions and thicknesses of each component shown in the drawings are arbitrary, and the present invention does not limit the dimensions and thicknesses of each component. To make the illustrations clearer, the thickness of some components has been appropriately exaggerated in the drawings.

[0028] like Figure 1 As shown, existing public goods game and network game methods are mostly based on ordinary graphs or homogeneous groups, which makes it difficult to express the high-order interaction structure of a public project involving multiple subjects or the same subject participating in multiple projects simultaneously. This invention proposes a networked system cooperative evolution measurement and resource optimization method based on hypergraph public goods game. This method represents subjects as hypergraph nodes and public goods projects as hyperedges. The participation relationship between subjects and public goods projects is described by the hypergraph association matrix. Furthermore, a repeated multi-person public goods game model is established by combining resource endowment, contribution ratio, productivity, and interaction continuation probability. Then, by comparing the full cooperation payoff with the deviation payoff of a single subject, the continuation probability threshold required for each subject to maintain full cooperation is calculated, and the system is judged to be in the full cooperation feasible range based on this.

[0029] Specifically, the collaborative optimization method for public resource allocation and use based on hypergraph game theory provided in this embodiment of the invention includes the following steps: S101: Construct a hypergraph public resource game model.

[0030] In the hypergraph public resource game model, hypergraph nodes are participating entities, and hyperedges are public resource projects. The participation relationship between participating entities and public resource projects is described by the hypergraph association matrix.

[0031] S103: Based on the Hypergraph public resource game model, calculate the payoffs of each participating entity under different cooperative states.

[0032] In this embodiment, the calculation of the benefits of each participating entity under different cooperative states includes the following sub-steps: S1031: Calculate the revenue of participating entities under a given contribution matrix based on the linear public goods revenue function; S1032: Construct three types of cooperative states, including the state in which all participating entities fully cooperate, the state in which some participating entities deviate from the cooperation while other participating entities maintain full cooperation, and the state in which none of the participating entities contribute. S1033: Calculate the revenue of participating entities under the three types of cooperation states. This revenue is used as the threshold for calculating the full cooperation of participating entities.

[0033] In this embodiment, the linear public good revenue function is:

[0034] in, as the main body Given a contribution matrix The following profits, as the main body Resource endowment, as the main body Participating in the A game of public resources as the main body Productivity parameters, as the main body In the The proportion of contribution to public resources, For the contribution matrix, For public resource identification, For the number of public resource games, For the number of participating entities, For super-edge size.

[0035] S105: Calculate the participants' revenue based on the linear public goods revenue function, and calculate the participants' threshold using the full cooperation maintenance condition under the Grim strategy.

[0036] In this embodiment, under the Grim policy, full cooperation is maintained under the following conditions:

[0037] in, remember To exclude the main body Maintain full cooperation with other entities, main body Deviating from the benefits of full cooperation The revenue when no entity contributes. The benefits when all parties cooperate fully. For the probability of continuation.

[0038] The threshold for participating entities is:

[0039] The threshold for cooperation among all participating entities in the system is:

[0040] in, as the main body Full cooperation threshold The threshold for cooperation among all participating entities.

[0041] S107: Optimize resource allocation and contribution strategies, and output resource allocation and individual contribution schemes that are conducive to maintaining full cooperation.

[0042] In this embodiment, when the continuation probability meets a preset condition, the resource endowment vector or contribution matrix is ​​adjusted to lower the overall cooperation threshold of all participating entities or expand the feasible range of full cooperation, thereby obtaining a resource allocation scheme and individual contribution scheme that are conducive to maintaining full cooperation. The preset condition is:

[0043] in, To maintain probability, The threshold for cooperation among all participating entities.

[0044] In this implementation, the optimization of resource allocation and contribution strategies includes the following sub-steps: S1071: Identify high-threshold nodes and determine optimization directions.

[0045] Based on the threshold calculation results of the participating entities, all participating entities are sorted, key entities that cause the overall system threshold to rise are identified, the thresholds of high-threshold entities are lowered, and the resource or contribution configurations of low-threshold entities are appropriately adjusted without compromising overall feasibility, so as to make the thresholds of each entity more balanced, thereby reducing the maximum threshold of the system.

[0046] S1072: Based on the participants' excess capacity, threshold size, and resource endowment, resource endowment is redistributed.

[0047] When redistributing resources, resources should be directed more towards participants or key hyper-edge related entities that can effectively reduce the overall cooperation threshold of all participants, thereby reducing the overall cooperation threshold of the system.

[0048] S1073: By adjusting the contribution matrix, the proportion of investment by participating entities in different public goods projects can be changed to promote full cooperation.

[0049] When adjusting the contribution matrix, participants with higher super-degree, more abundant resources, or higher cooperation stability are guided to allocate more contributions to the super-edges where participants with lower average super-degree, higher cooperation risk, or higher threshold reside.

[0050] Compared with existing technologies, the collaborative optimization method for public resource allocation and use based on hypergraph game theory provided by this invention has the following technical effects: 1. Existing methods for public goods game theory and network game theory are mostly based on ordinary graphs or homogeneous groups, which are difficult to express the high-order interaction structure of a public project involving multiple stakeholders or the same staker participating in multiple projects simultaneously. This invention proposes a hypergraph-based modeling framework for repeated multi-stakeholder public goods game theory, using stakeholders as nodes and public goods projects, governance alliances, or collaborative groups as hyperedges. It represents the participation relationship between stakeholders and projects through an association matrix and introduces resource endowment, contribution matrix, project productivity, and continuation probability. This framework can fully preserve the interaction and overlapping participation information of multiple stakeholders, avoiding structural distortion caused by breaking down high-order collaborative relationships into binary edges.

[0051] 2. Existing technologies struggle to directly determine whether a complex networked system can maintain full cooperation, typically relying on extensive simulations and lacking calculable and interpretable stability criteria. This invention proposes a method for calculating the feasible interval of full cooperation and the node-level continuation probability threshold. Under full cooperation, the difference in returns for each agent maintaining full commitment versus unilateral deviation is calculated, yielding the thresholds required for agents to maintain cooperation and the system's full cooperation threshold. This transforms the cooperation stability problem into a threshold comparison problem, enabling rapid identification of the feasibility of full cooperation and the bottleneck agents most prone to deviating from cooperation.

[0052] 3. Existing average resource allocation techniques may be effective in homogeneous networks, but in heterogeneous hypergraphs, they may increase the incentive for some entities to deviate, failing to guarantee optimal overall cooperation. This invention proposes a differentiated resource allocation optimization method for policymakers. Under total resource constraints and non-negativity constraints, it aims to minimize the system threshold or maximize the overall cooperation feasibility margin by solving for the resource endowment vector. This prioritizes resource compensation for the entities or groups that have the greatest impact on the system cooperation threshold, expanding the overall cooperation feasibility interval and improving the success rate of public governance or resource coordination.

[0053] 4. Existing technologies that only adjust initial resource allocation cannot address how individuals use resources across multiple public goods projects, and lack actionable contribution suggestions for participating entities. This invention proposes an individual contribution matrix optimization method. Under each entity's budget constraints, it optimizes the proportion of investment by the entity in different hyperedge projects, thereby lowering the cooperation threshold for low-stability or critical projects. Simultaneously, it promotes sustainable cooperation from both the managerial resource allocation and individual resource usage levels, making it applicable to scenarios such as climate governance, water resource sharing, and renewable resource management.

[0054] The present invention will now be described in detail with reference to preferred embodiments.

[0055] To address the difficulty of maintaining cooperation in public governance, resource sharing, and group collaboration using existing technologies, this invention proposes a method for measuring the evolution of cooperation in networked systems and optimizing resources based on hypergraph public goods game theory. This method represents subjects as hypergraph nodes and public goods projects as hyperedges, using a hypergraph association matrix to describe the participation relationships between subjects and public goods projects. Furthermore, it establishes a repeated multi-player public goods game model by combining resource endowment, contribution ratio, productivity, and interaction continuation probability. Finally, by comparing the overall cooperation payoff with the deviation payoff of a single subject, it calculates the continuation probability threshold required for each subject to maintain full cooperation, and determines whether the system is within the feasible range of full cooperation.

[0056] The model of this invention can be briefly represented as follows. Assume the system has... individual entities and A public goods game, with the following set of participants. The public goods game set is The participation relationships between entities and public goods in the game are represented by the correlation matrix. It means that, among them Representing the subject Participating in the A public goods game 0 indicates non-participation. Main body The resource endowment is The contribution ratio is and satisfy .

[0057] In the case of linear public goods revenue, the main body The profit can be expressed as: .

[0058] in, Indicates the size of the superedge. Representing the subject The productivity parameters are: the first term represents the revenue that the entity receives from public goods projects, and the second term represents the revenue that the entity receives from retaining uninvested resources.

[0059] This invention employs the Grim strategy to analyze whether full cooperation can be maintained. To exclude the main body Maintain full cooperation with other entities, main body Deviating from the benefits of full cooperation; The revenue when no entity contributes; The benefits when all parties cooperate fully.

[0060] Full cooperation can be sustained if the following conditions are met: .

[0061] From this, we can obtain the main body. The threshold for perfect cooperation. In the case of heterogeneous productivity, this threshold can be expressed as: .

[0062] The threshold for all individuals in the system to cooperate is When the actual continuation probability satisfies When the system is in a fully cooperative and feasible state, it is in a cooperative and feasible state; otherwise, the system is at risk of cooperative instability.

[0063] The method provided by this invention includes the following four steps: Step 1: Construct a hypergraph public goods game model.

[0064] Obtain the set of subjects, the set of public goods games, and the participation relationships between subjects and public goods games, and construct an association matrix. Enter resource endowment Contribution ratio Productivity parameters super-scale and the probability of continuation .

[0065] Step 2: Revenue Calculation.

[0066] Based on the hypergraph incidence matrix obtained in step 1 Resource endowment vector Contribution matrix Productivity parameters or and super-edge size Calculate the benefits of each entity under different cooperative states.

[0067] Specifically, firstly, the subject is calculated based on the linear public goods revenue function. Given a contribution matrix The following benefits:

[0068] Secondly, three types of states are constructed respectively: the state in which all subjects cooperate fully {1}, the state in which all subjects cooperate fully ... Other entities maintain full cooperation while the main body A state of deviation from cooperation }, and the state {0} where none of the subjects contribute; Finally, calculate separately , and .

[0069] in, Representing the subject Benefits obtained in a fully cooperative state This represents the benefit gained by subject i when it unilaterally deviates from full cooperation. This represents the benefit of subject i when all subjects contribute nothing. These three types of benefits provide the basis for subsequent calculations of the threshold for full subject cooperation.

[0070] Step 3: Calculate the full cooperation threshold.

[0071] The payoffs of agents under the states of full cooperation, single-agent deviation, and total non-contribution are calculated based on the payoff function. The threshold for each agent is then calculated using the full cooperation maintenance condition under the Grim policy. The system threshold is then obtained. .

[0072] Step 4: Optimize resource allocation and contribution strategies.

[0073] when At that time, in order to reduce Or, with the goal of expanding the feasible range of full cooperation, adjust the resource endowment vector. or contribution matrix This will lead to a resource allocation scheme and individual contribution scheme that are conducive to maintaining full cooperation.

[0074] The specific process is as follows: 1) Identify high-threshold nodes and determine optimization directions.

[0075] Based on the threshold of each subject The calculation results are used to sort all subjects and identify those that cause the overall system threshold. The key actors with higher thresholds are those with higher thresholds. Higher thresholds indicate that actors are more likely to deviate from full cooperation given their current resource endowments and contribution structures; lower thresholds indicate that the conditions required for them to maintain full cooperation are relatively relaxed. Therefore, the basic direction of optimization is to reduce the risk of high-threshold actors. Furthermore, without compromising overall feasibility, the resource or contribution allocation of low-threshold entities can be appropriately adjusted to make the thresholds of each entity more balanced, thereby reducing the system's maximum threshold. .

[0076] 2) Reduce the overall threshold by redistributing resources based on resource endowment.

[0077] From the threshold expression: It can be seen that the main body The threshold is also affected by its own resource endowment. ,productivity The number of participating hyperedges and the contributions of other entities to relevant public goods projects are also considered. Entities with higher hyperedge participation have more public goods projects under their belt and thus a stronger influence on the stability of cooperation across multiple hyperedges. Conversely, entities with lower hyperedge participation have relatively limited access to external cooperation support and are more likely to become weak points in cooperation. Therefore, resource endowments can be assessed based on entity hyperedge participation, threshold size, and resource endowment. Redistribute resources so that more of them can be directed toward areas where costs can be effectively reduced. The main body or key hyperedge associated entity, thereby reducing the overall system full cooperation threshold.

[0078] 3) Promote full cooperation based on contribution matrix adjustment.

[0079] With the total resources of the main body remaining unchanged, the contribution matrix can also be adjusted. Change the proportion of investment by the main entity in different public goods projects. From the denominator, we can see that other subjects are in the subject The greater the contribution to public goods projects, the greater the main body The lower the threshold required to maintain full cooperation, the better. Therefore, entities with higher excess levels, more abundant resources, or higher cooperation stability can be guided to allocate more contributions to the hyperedges where entities with lower average excess levels, higher cooperation risks, or higher thresholds reside. This adjustment of contribution proportions can improve the effective contribution level in key public goods projects, reduce the deviation motivation of high-risk entities, and thus lower the overall threshold. This increases the likelihood of the system maintaining full cooperation.

[0080] The following describes the process in detail using several embodiments.

[0081] Example 1: Analysis of Climate Fund Collaboration in Climate Commons Governance.

[0082] like Figure 2 As shown, in this embodiment, step S1, hypergraph construction, is specifically implemented as follows: Suppose we need to analyze the cooperative relationships among multiple countries surrounding projects such as the International Climate Fund, the Emissions Reduction Fund, the Climate Adaptation Fund, and the Technical Assistance Fund. The system first treats countries or regions as hypergraph nodes, and each climate fund or climate cooperation project as a hyperedge. If countries... Participating in the Climate Fund Then record If the country If you did not participate in the fund, then it will be recorded as follows: This yields the country-climate fund correlation matrix A. The resource endowment of country i... Its contribution ratio can be determined by its total investment in the entire climate fund, its committed contribution, or the normalized size of the climate fund; Can be by the state For the The proportion of each climate fund's investment to its total climate finance is determined; productivity parameters. or The criteria can be determined based on the efficiency of fund implementation, the emission reduction effect of projects, or climate governance capabilities. In this step, a country can participate in multiple climate funds simultaneously, and a climate fund can also include multiple countries, thus forming a hypergraph structure with multiple stakeholders and intertwined projects.

[0083] Step S2 calculates the revenue, and its specific implementation is as follows: The system uses the correlation matrix obtained in step 1 Resource endowment vector and contribution matrix This calculates the benefits for each country under different climate fund cooperation scenarios. For each country... In this regard, its public benefits come from the feedback benefits of all national contributions to the climate fund in which it participates, amplified through productivity gains, while its retained benefits come from national contributions. Funds held back by countries that have not contributed to the Climate Fund. The system constructs three states: the first is a fully cooperative state where all countries have contributed all climate funds as committed; the second is a state where all countries have contributed as committed; and the third is a state where all countries have not contributed. In addition to maintaining full cooperation with other countries, the country The first category represents a single entity's deviation from the Climate Fund, characterized by reducing or withdrawing from its contributions; the second category represents a situation where no country contributes to the Climate Fund. The system calculates these separately. , and This serves as the input for subsequent threshold determination.

[0084] Step S3 determines the threshold, the core of which is to assess whether a country has the incentive to continue climate finance cooperation. The system substitutes the three types of benefits obtained in Step 2 into the full cooperation maintenance condition under the Grim strategy to calculate the threshold for each country. and take This serves as the overall threshold for the climate commons governance system. If the actual probability of continuation... Greater than or equal to This indicates that full cooperation can be maintained under the current climate finance structure; if Less than This indicates that at least one country has a strong incentive to reduce investment in or withdraw from some climate projects. At this point, The largest country can be identified as a key risk entity in this climate cooperation network, and the climate funds associated with it can be identified as key risk projects.

[0085] Step S4.1 involves resource optimization, which is implemented as follows: When the system determines At that time, the resource optimization module is based on each country The ranking results are used to identify bottleneck countries or bottleneck climate funds that are causing the overall threshold to rise. With the total climate finance size remaining constant, the system can recommend that international organizations, fund managers, or policymakers appropriately increase financial support for bottleneck countries or key climate projects, thereby reducing short-term deviation returns or increasing long-term cooperation returns, and thus lowering... .

[0086] Step S4.2 involves adjusting the contribution, which is implemented as follows: With total national contributions remaining constant, the system further adjusts the proportion of national contributions among different climate funds. For example, if certain climate funds have fewer participating countries, lower average super-contributions, or are highly correlated with high-threshold countries, the system can suggest that countries with more resources or higher cooperation stability allocate more funds to these funds. This can increase the effective contribution level in key super-borders and reduce the deviation incentives of high-risk countries.

[0087] Step S5 evolution simulation, its specific implementation is as follows: The system takes the resource endowment vectors and contribution matrices before and after optimization as inputs, respectively, to simulate multiple rounds of climate finance cooperation, and outputs... Changes include changes in bottleneck countries, changes in key funds, and changes in long-term cooperation rates. If optimized... The decrease in the number of full-cooperation maintenance rounds and the increase in the number of rounds in the simulation indicate that the resource allocation and contribution adjustment scheme can improve the cooperative stability of climate commons governance.

[0088] Example 2: Analysis of watershed governance cooperation in cross-regional water resource sharing.

[0089] like Figure 2 As shown, step S1, hypergraph construction, is specifically implemented as follows: Suppose we need to analyze the cooperative relationships formed by multiple countries or regions regarding transboundary rivers, cross-regional watershed management, water pollution prevention, and water infrastructure maintenance. The system uses national, regional, or watershed management entities as nodes, and each transboundary river or jointly managed watershed as a hyperedge. If the entities... Participate in river or watershed projects The governance, then recorded Otherwise remember .main body resource endowment The contribution ratio can be determined by GDP allocation, water governance budget, international water-related aid funds, or watershed governance commitments. Can be the main body Thrown into the river The governance funds, maintenance costs, or governance responsibilities allocated according to the proportion of river flow are determined; productivity parameters can be determined by the efficiency of water governance project implementation, water quality improvement efficiency, or government governance capacity indicators.

[0090] Step S2, the revenue calculation, is implemented as follows: The system is based on the subject-river correlation matrix and contribution matrix Calculate the benefits of each entity in watershed management. For each entity... Its public benefits come from water quality improvement, flood risk reduction, infrastructure maintenance, and regional ecological benefits resulting from joint watershed management investments; its retained benefits come from funds retained for projects not invested in management. The system calculates the benefits when all stakeholders invest management resources as promised, and the benefits for each stakeholder. The benefits of unilaterally reducing investment in the management of relevant rivers, and the benefits of all stakeholders not investing in management.

[0091] Step S3, threshold determination, is essentially about identifying the weaker stakeholders in watershed cooperation.

[0092] The system calculates for each entity. and obtain For example, if a country participates in fewer rivers, has lower resource endowments, or if other stakeholders in the rivers it participates in contribute insufficiently, then that country... The higher value suggests that it is easier to reduce investment under the current governance structure. The system will... Higher-risk entities and their associated river projects are marked as priority intervention targets.

[0093] Step S4.1 Resource optimization, specifically implemented as follows: When In such cases, the river basin commission, higher-level coordinating body, or international organization may adjust compensation funds, infrastructure assistance, or governance budgets based on the system output. For example, compensation funds may be appropriately increased for entities with heavy governance responsibilities but low resource endowments; governance resources may be prioritized for critical rivers that simultaneously affect multiple high-threshold entities. These adjustments are intended to lower the overall threshold. This will improve the feasibility of continuous investment of governance resources by various stakeholders.

[0094] Step S4.2, contribution adjustment, is implemented as follows: With the total governance resources of each entity remaining unchanged, the system can suggest that entities reallocate their investment proportions across multiple rivers. For example, more governance funds can be invested in river projects with lower average participation, higher cooperation risks, or greater impact on system thresholds; for rivers with higher cooperation stability, marginal investment can be appropriately reduced. In this way, the level of effective cooperation in key watersheds can be improved.

[0095] Step S5, evolution simulation, is implemented as follows: The system simulates multiple rounds of watershed governance cooperation before and after optimization, recording whether cooperation can be maintained, the average convergence time, changes in bottleneck entities, and changes in key rivers. If the number of high-threshold entities decreases after optimization, and the full cooperation state remains stable in more rounds, it indicates that the scheme can improve the governance stability of cross-regional water resource sharing.

[0096] Example 3: Analysis of fishery resource cooperation in renewable resource management.

[0097] like Figure 2 As shown, step S1, hypergraph construction, is specifically implemented as follows: Taking fishery resource management as an example, the system uses national, regional, enterprise, or resource management agency as the main nodes, and fishery grounds jointly fished, protected, or restored as super-borders. If the main... In the fishing grounds If there is a relationship of fishing, protection, subsidy or restoration investment, then it is recorded as... Otherwise remember .main body resource endowment The contribution ratio can be determined by fisheries subsidies, sustainable fisheries recovery investments, resource management budgets, or related fiscal expenditures. Can be the main body In the fishing grounds The proportion of the catch to the total catch, the proportion of restoration input, or the proportion of regulatory input are used to determine the productivity parameters; the productivity parameters can be determined by government effectiveness, resource restoration efficiency, regulatory enforcement, or ecological restoration benefits.

[0098] Step S2, the revenue calculation, is implemented as follows: The system calculates the common revenue and retention revenue of each entity in different fishing grounds based on the country-fishing ground hypergraph. For an entity that participates in the management of multiple fishing grounds, its input allocation will affect the cooperative stability of multiple hyperedges; for a fishing ground shared by multiple entities, any entity reducing recovery input or increasing short-term fishing may change the revenue expectations of other participating entities. Therefore, the system calculates the revenue under three states: full cooperation, single-entity deviation, and no contribution from all entities.

[0099] Step S3, threshold determination, focuses on identifying the sources of risk from overexploitation or insufficient recovery investment. The system calculates the thresholds for each entity. And obtained When there are many participants in a fishing ground but their average contribution is insufficient, or when some participants have low resource endowments but bear the management responsibility for multiple fishing grounds, the corresponding participants or fishing grounds will exhibit higher cooperation risks. Based on this, the system identifies the participants most likely to deviate from full cooperation and the fishing grounds most in need of governance intervention.

[0100] Step S4.1 Resource optimization, the specific implementation of which is as follows: Given a fixed total subsidy or total governance budget, the system recommends allocating more resources to [the relevant government departments / organizations]. Significantly affected entities or fishing grounds. For example, increase governance support for fishing grounds with high recovery pressure, heavy responsibilities of participating entities, or low stability of cooperation, in order to reduce the deviation motivation of relevant entities and reduce the risk of overfishing.

[0101] Step S4.2 contribution adjustment, the specific implementation of which is as follows: Under the condition that the total budget remains unchanged, the system adjusts its contribution ratio among different fishing grounds. For fishing grounds with high cooperative stability, marginal input can be appropriately reduced; for fishing grounds with low cooperative stability, low average yield, or those more prone to full cooperative failure, the proportion of recovery input or regulatory input is increased, thereby improving the overall level of sustainable management.

[0102] Step S5 evolution simulation, its specific implementation is as follows: The system compares the full cooperation threshold, key stakeholders, key fishing grounds, and long-term cooperation rate before and after optimization to assess the improvement effect of resource optimization and contribution adjustment on fishery resource governance. If the optimization... The decrease in costs, the increase in the stability of cooperation in key fishing grounds, and the rise in the long-term cooperation rate indicate that this method can improve the overall cooperative feasibility of renewable resource governance without increasing the total budget.

[0103] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A collaborative optimization method for the allocation and use of public resources based on hypergraph game theory, characterized in that, The method includes the following steps: S101: Construct a hypergraph public resource game model. In the hypergraph public resource game model, hypergraph nodes are participating entities, and hyperedges are public resource projects. The participation relationship between the participating entities and the public resource projects is described by the hypergraph association matrix. S103: Based on the hypergraph public resource game model, calculate the payoffs of each participating entity under different cooperative states; S105: Calculate the revenue of the participating entity based on the linear public goods revenue function, and calculate the threshold of the participating entity using the full cooperation maintenance condition under the Grim strategy; S107: Optimize resource allocation and contribution strategies, and output resource allocation and individual contribution schemes that are conducive to maintaining full cooperation.

2. The collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 1, wherein step S103 includes the following sub-steps: S1031: Calculate the revenue of the participating entity under a given contribution matrix based on the linear public goods revenue function; S1032: Construct three types of cooperative states, including the state in which all participating entities fully cooperate, the state in which some participating entities deviate from the cooperation while other participating entities maintain full cooperation, and the state in which none of the participating entities contribute. S1033: Calculate the revenue of the participating entities under the three types of cooperative states, and use the revenue as the threshold for calculating the full cooperation of the participating entities.

3. The collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 2, wherein the linear public good revenue function is: in, as the main body Given a contribution matrix The following profits, as the main body Resource endowment, as the main body Participating in the A game of public resources as the main body Productivity parameters, as the main body In the The proportion of contribution to public resources, For the contribution matrix, For public resource identification, For the number of public resource games, For the number of participating entities, For super-edge size.

4. In the collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 3, in step S105, under the Grim policy, full cooperation is maintained under the following condition: in, remember To exclude the main body Maintain full cooperation with other entities, main body Deviating from the benefits of full cooperation The revenue when no entity contributes. The benefits when all parties cooperate fully. For the probability of continuation.

5. The collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 4, wherein the threshold for the participating entities is: The threshold for cooperation among all participating entities in the system is: in, as the main body Full cooperation threshold The threshold for cooperation among all participating entities.

6. The collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 5, in step S107, when the continuation probability meets a preset condition, the resource endowment vector or contribution matrix is ​​adjusted to reduce the overall cooperation threshold of all participating entities or expand the feasible interval of full cooperation, thereby obtaining a resource allocation scheme and individual contribution scheme that are conducive to maintaining full cooperation. The preset condition is: in, To maintain probability, The threshold for cooperation among all participating entities.

7. The collaborative optimization method for public resource allocation and use based on hypergraph game theory as described in claim 6, wherein step S107 includes the following sub-steps: S1071: Identify high-threshold nodes and determine optimization directions; S1072: Based on the extent, threshold size, and resource endowment of the participating entities, the resource endowment is redistributed; S1073: By adjusting the contribution matrix, the proportion of investment by the participating entities in different public goods projects is changed to promote full cooperation.

8. The collaborative optimization method for public resource allocation and use based on hypergraph game as described in claim 7, in step S1071, according to the threshold calculation results of the participating subjects, all the participating subjects are sorted, key subjects that cause the overall threshold of the system to rise are identified, the threshold of high-threshold subjects is reduced, and the resource or contribution configuration of low-threshold subjects is appropriately adjusted without destroying the overall feasibility, so that the thresholds of each subject are more balanced, thereby reducing the maximum threshold of the system.

9. The collaborative optimization method for public resource allocation and use based on hypergraph game as described in claim 8, in step S1072, when redistributing resource endowments, resources are directed more towards the participating entities or key hyperedge-related entities that can effectively reduce the overall cooperation threshold of all participating entities, thereby reducing the overall cooperation threshold of the system.

10. The collaborative optimization method for public resource allocation and use based on hypergraph game as described in claim 9, in step S1073, when adjusting the contribution matrix, the participating entities with larger superdegree, more abundant resources, or higher cooperation stability are guided to allocate more contributions to the hyperedges where entities with lower average superdegree, higher cooperation risk, or higher threshold are located.

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